Embodiments of the invention generally pertain to systems and methods for processing streams of user data for applications including data recording and data communication. In particular, embodiments of the invention pertain to systems and methods for encoding and decoding streams of data.
Linear block codes, such as Single Parity Check (SPC) codes, have found wide-spread application in areas such as magnetic recording and data communications in recent years. Such codes are often used with a Viterbi detector, which provides a coding gain by using a constraint associated with the code to remove certain data sequences from being considered as possible decodings of a received data stream. As used herein, the term “coding gain” refers to a code's ability to lessen the occurrences of errors associated with communication and/or storage of information. The performance of such a detector generally improves when linear block codes with shorter input block lengths are used. However, codes with shorter input block lengths tend to require higher overhead, thus reducing the code rate and resulting in a performance tradeoff of coding gain versus code rate penalty. As used herein, “code rate penalty” refers to a measure (e.g., a ratio) of an amount of user data relative to an amount of extra coding information that is associated with the user data. Extra coding information may be used to detect and/or correct errors that may occur in user data. This extra coding information is commonly referred to as “redundant information/data” or “parity information/data.”
Tensor Product Codes (TPC) allow the use of shorter input block lengths without the full code rate penalty typically associated with such block lengths. Accordingly, there is a continued interest in improving the performance of TPC-based encoding and decoding systems.